I have a Logitech H390 USB headset/microphone which I think is amazing. The result of the microphone input is very crisp, crystal clear. But this also poses a problem. Along with my speaking voice, I can also hear my mouth sounds in the audio result (smacking of the lips and tongue). In other words, the microphone seems to be picking up "too much".
 
Is there any strategic way to cancel out these sounds while maintaining the clear spoken output?

Start with some equalization - roll off those highs!

Maybe a pop filter? Some foam wrapped around the mic?

Those mics are really all about midrange. The only thing I can think of is to do what bittflipper suggested, and move the mic farther away from your mouth. It's probably way too close.

It probably has a gate built-in, which accentuates the lip smacks etc. if they are loud enough to trigger.  If you move it farther away, you might have trouble triggering anything but the loudest singing.  And as pointed out above, if it is a headphone mic set it is for VO, probably a little electric condenser, it is all midrange.  You can get a better sound w/ a real mic, even dynamic.  Just do the telephone EQ trick but back off the cut off points and depth until you get a fuller but not too full sound.  One thing about headphone mics, they will cut.
 
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